A034739 Dirichlet convolution of b_n=2^(n-1) with Catalan numbers.

1, 3, 6, 15, 30, 82, 196, 575, 1694, 5418, 17820, 60986, 212108, 751420, 2690912, 9728639, 35423206, 129779210, 477900844, 1767797906, 6565169652, 24468398788, 91486757944, 343068124346, 1289920924764, 4861980376004